On Friday alone, Avast detected up to 52,000 attacks from the ransomware, most of which were targeting Russia, Ukraine and Taiwan.
The malicious software - called "ransomware" because it encrypts systems and threatens to destroy data if a $300 Bitcoin (NZ$430) ransom is not paid - is spreading among computers that have not been patched, experts said.
"We are now seeing more than 75,000 detections.in 99 countries", Jakub Kroustek of the security firm Avast said in a blog post.
By Kaspersky Lab's count, the malware struck at least 74 countries.
Forcepoint Security Labs said that "a major malicious email campaign" consisting of almost five million emails per hour was spreading the new ransomware.
According to Wired, the ransomware strain WannaCry (also known as WanaCrypt0r and WCry) has gained particular traction in Spain, where it has hobbled the telecom company Telefonica, the natural gas company Gas Natural, and the electrical company Iberdrola.
"This is not targeted at the NHS, it's an global attack and a number of countries and organisations have been affected", she added.
"Seeing a large telco like Telefonica get hit is going to get everybody anxious".
Most of the affected hospitals were in England, but several facilities in Scotland also reported being hit.
Only a small number of US -headquartered organizations were hit because the hackers appear to have begun the campaign by targeting organizations in Europe, said Vikram Thakur, research manager with security software maker Symantec.
Britain's National Cyber Security Centre and its National Crime Agency were looking into the United Kingdom incidents.
Computers of companies such as shipper FedEx and government services such as Britain's National Health Service were inflected by "ransomware" demanding payments of as much as Dollars 600 in Bitcoin currency to restore access and scrambling data, Reuters reported.
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It demands payment in three days or the price is doubled, and if none is received in seven days, the files will be deleted, according to the screen message.
The malware was made available online on April 14 through a dump by a group called Shadow Brokers, which claimed a year ago to have stolen a cache of "cyber weapons" from the National Security Agency (NSA).
If it is the same vulnerability involved in the latest attack, this will raise serious questions for IT officials at the top of NHS trusts, who may have missed a critical security update and failed to patch the vulnerability, leading to severe consequences nearly two months later.
Essentially, the only way to prevent a computer on a compromised network being hit by the ransomware is to turn it off or shut down the network.
"The age-old advice is to never click on a link in an email".
NHS Incident Director Anne Rainsberry urged the British public to "use the NHS wisely while we deal with this major incident which is still ongoing".
Ransom demands have been reported from more than 70 countries so far.
"Ransomware becomes particularly nasty when it infects institutions like hospitals, where it can put people's lives in danger", said Kroustek, the Avast analyst.
The Barts Health group, which manages major central London hospitals including The Royal London and St Bartholomew's, said it had activated a major incident plan and had canceled routine appointments. The program recommends certain patients for treatment with specialists and has a two-week availability window before the treatment is canceled.
Caroline Brennan, 41, went to the hospital to see her brother, who had open heart surgery.
Speaking ahead of the Cobra meeting in Whitehall at 2.30pm, she told Sky News: "It is disappointing that they have been running Windows XP - I know that the Secretary of State for Health has instructed them not to and most have moved off it".
Users should regularly back up their data and ensure that security updates are installed on your computer as soon as they are released.
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